Complex Analysis on Riemann Surfaces

Quasi Riemann surfaces

A quasi Riemann surface is defined to be a certain kind of complete metric space Q whose integral currents are analogous to the integral currents of a Riemann surface. In particular, they have properties sufficient to express Cauchy-Riemann equations on Q. The prototypes are the spaces D 0 (Σ)m of integral 0-currents of total mass m in a Riemann surface Σ (usually called the integral 0-cycles o...

Automatic Generation of Riemann Surface Meshes

Riemann surfaces naturally appear in the analysis of complex functions that are branched over the complex plane. However, they usually possess a complicated topology and are thus hard to understand. We present an algorithm for constructing Riemann surfaces as meshes in R from explicitly given branch points with corresponding branch indices. The constructed surfaces cover the complex plane by th...

Tenth Prairie Analysis Seminar

If we have a real vector field in the plane, the integral curves foliate the plane. Similarly, if we have a complex vector field in C then the complex integral curves foliate space by Riemann surfaces. An example of a question one might ask, is whether these Riemann surfaces are dense in space. In the case of vector fields in the plane, this is impossible, but if we do it on a torus instead, it...

Complex Analysis on Riemann Surfaces

Complex Analysis on Riemann Surfaces